
where \(a_0={3.35}{}\)  is the interlayer spacing of bulk graphite.
The TB parameters were fit to electronic band structures of single and double-wall carbon nanotubes obtained from first-principles density functional theory. We first fix the pp\(\pi \)  parameters of the intra-layer interaction by fitting to the band structure of graphene, to reproduce correct behavior in the limit of very large nanotubes. Next, we fix the pp\(\sigma \)  parameters of the intra-layer interaction to reproduce the ab initio bands of nanotubes with radii between 5.26.2: (9,9), (16,0) and (9,6) (SI-Fig. ). Lastly, we optimize the the interlayer parameters to reproduce the ab initio bands of two DWNTs: (16,0)@(24,0) and (9,6)@(15,10). The optimized parameters are summarized in Table REF .
The transmission and density of states (DOS) are extracted using the
Landauer-Büttiker formalism (LB)
formalism [1]} as implemented in TBTrans [2]}. All calculations are performed at zero voltage between the two electrodes.
<TABLE>